Finite Group Databasebeta

← #120928

Subgroups — #120928

Order 512.

553 conjugacy classes of subgroups.

The subgroup lattice has 409 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21943C211yesmaximal, characteristic
2#8108C211yesmaximal, characteristic
3#8104C211yesmaximal, characteristic
4#8051C211yesmaximal, characteristic
5#8009C211yesmaximal, characteristic
6#7942C211yesmaximal, characteristic
7#7929C211yesmaximal, characteristic
8C2×#407C2211yescharacteristic
9C2×#407C2211yescharacteristic
10C2×#407C2211yescharacteristic
11C2×#407C2211yescharacteristic
12#2280C2211yescharacteristic
13#2280C2211yescharacteristic
14C2×C4×C22⋊C4C2211yescharacteristic
15#1854—22no—
16#1854—22no—
17#1809—22no—
18#1305—22no—
19#1305—22no—
20#1297—22no—
21#1293C414yescomplemented
22#1284—22no—
23#1282—22no—
24C24×C4C2311yescharacteristic
25C22×M16—21no—
26C22×M16—21no—
27C22×M16—21no—
28C22×M16Q811yescharacteristic
29C22×M16Q811yescharacteristic
30C2×#117—21no—
31C2×#117—21no—
32C22×C22⋊C4—21no—
33C22×C42—21no—
34C2×#107—22no—
35C2×#106—22no—
36#407—21no—
37#407—21no—
38#407—21no—
39#407—21no—
40#407—21no—
41#407—21no—
42#407—21no—
43#407—21no—
44#407—21no—
45#407—21no—
46#407—21no—
47#407—21no—
48#407—21no—
49#407C2×C412yes—
50#407C2×C412yes—
51#407Q812yes—
52C2×C22⋊C8—21no—
53C2×C22⋊C8—21no—
54C2×C22⋊C8—21no—
55C2×C22⋊C8—21no—
56C2×C22⋊C8—21no—
57C2×C22⋊C8—21no—
58C2×C22⋊C8C2×C412yes—
59C2×C22⋊C8D412yes—
60#381—21no—
61#381—21no—
62#380—21no—
63#380—21no—
64#380D412yes—
65#380D412yes—
66#379—21no—
67#379—21no—
68C4×C22⋊C4—21no—
69C4×C22⋊C4—21no—
70C4×C22⋊C4—21no—
71C4×C22⋊C4—21no—
72C4×C22⋊C4—21no—
73C4×C22⋊C4—21no—
74C4×C22⋊C4—21no—
75C4×C22⋊C4D412yes—
76C2×#95—21no—
77#340—24no—
78C25#4111yescharacteristic
79C23×C4—41no—
80C23×C4—81no—
81C23×C4—81no—
82C23×C4C22×C411yescharacteristic
83C23×C4C2×D411yescharacteristic
84C23×C4C2×D411yescharacteristic
85C23×C4C2×D411yescharacteristic
86C23×C4C2×D411yescharacteristic
87C23×C4C2×Q811yescharacteristic
88C23×C4C2×Q811yescharacteristic
89C23×C4#4111yescharacteristic
90C23×C4#4111yescharacteristic
91C23×C4#4111yescharacteristic
92C23×C4#4111yescharacteristic
93C23×C4#4111yescharacteristic
94C23×C4#4111yescharacteristic
95C23×C4#4111yescharacteristic
96C2×M16—22no—
97C2×M16—22no—
98C2×M16—22no—
99C2×M16—21no—
100C2×M16—21no—
101C2×M16—21no—
102C2×M16—21no—
103C2×M16—41no—
104C2×M16—41no—
105C2×M16—41no—
106C2×M16—81no—
107C2×M16—81no—
108C2×M16—81no—
109C2×M16—81no—
110C2×M16—81no—
111C2×M16—81no—
112C2×M16—81no—
113C2×M16—81no—
114C22×C8—22no—
115C22×C8—22no—
116C22×C8—21no—
117C22×C8—21no—
118C22×C8—41no—
119#117—81no—
120#117—81no—
121#117—81no—
122#117—81no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4—22no—
125C2×C22⋊C4—22no—
126C2×C22⋊C4—22no—
127C2×C22⋊C4—22no—
128C2×C22⋊C4—44no—
129C2×C22⋊C4—41no—
130C2×C22⋊C4—41no—
131C2×C22⋊C4—41no—
132C2×C22⋊C4—41no—
133C2×C22⋊C4—41no—
134C2×C42—22no—
135C2×C42—41no—
136C2×C42—41no—
137C2×C42—41no—
138C2×C42—81no—
139C2×C42—81no—
140#107—82no—
141#106—82no—
142C22⋊C8—22no—
143C22⋊C8—22no—
144C22⋊C8—22no—
145C22⋊C8—22no—
146C22⋊C8—22no—
147C22⋊C8—22no—
148C22⋊C8—22no—
149C22⋊C8—41no—
150C22⋊C8—41no—
151C22⋊C8—41no—
152C22⋊C8—41no—
153C22⋊C8—41no—
154C22⋊C8—41no—
155C22⋊C8—41no—
156C22⋊C8—41no—
157C22⋊C8C4⋊C414yes—
158#95—22no—
159#95—22no—
160#95—22no—
161#95—41no—
162#95—41no—
163#95—41no—
164C24—42no—
165C24—81no—
166C24—81no—
167C24C4×Q811yescharacteristic
168C24#12111yescharacteristic
169C24#12311yescharacteristic
170C24#12311yescharacteristic
171C24#12511yescharacteristic
172C24#12611yescharacteristic
173C24#12611yescharacteristic
174C22×C4—41no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4—41no—
178C22×C4—41no—
179C22×C4—41no—
180C22×C4—41no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—41no—
184C22×C4—41no—
185C22×C4—41no—
186C22×C4—41no—
187C22×C4—41no—
188C22×C4—44no—
189C22×C4—42no—
190C22×C4—42no—
191C22×C4—42no—
192C22×C4—81no—
193C22×C4—81no—
194C22×C4—81no—
195C22×C4—81no—
196C22×C4—81no—
197C22×C4—81no—
198C22×C4—81no—
199C22×C4—82no—
200C22×C4—82no—
201C22×C4C2×C4⋊C411yescharacteristic
202C22×C4#11711yescharacteristic
203C22×C4#11711yescharacteristic
204C22×C4C4×D411yescharacteristic
205C22×C4C4×D411yescharacteristic
206C22×C4C4×D411yescharacteristic
207C22×C4#12011yescharacteristic
208C22×C4#12111yescharacteristic
209C22×C4#12111yescharacteristic
210C22×C4C22⋊Q811yescharacteristic
211C22×C4C22⋊Q811yescharacteristic
212C22×C4C22⋊Q811yescharacteristic
213C22×C4C22⋊Q811yescharacteristic
214C22×C4C22⋊Q811yescharacteristic
215C22×C4#12311yescharacteristic
216C22×C4#12311yescharacteristic
217C22×C4#12311yescharacteristic
218C22×C4#12411yescharacteristic
219C22×C4#12411yescharacteristic
220C22×C4#12411yescharacteristic
221C22×C4#12411yescharacteristic
222C22×C4#12511yescharacteristic
223C22×C4#12511yescharacteristic
224C22×C4#12511yescharacteristic
225C22×C4#12511yescharacteristic
226C22×C4#12611yescharacteristic
227C22×C4#12611yescharacteristic
228C22×C4C4⋊Q811yescharacteristic
229M16—82no—
230M16—82no—
231M16—81no—
232M16—81no—
233M16—81no—
234M16—81no—
235M16—82no—
236M16—81no—
237M16—81no—
238M16—81no—
239M16—81no—
240M16—82no—
241C2×C8—24no—
242C2×C8—42no—
243C2×C8—42no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—82no—
249C2×C8—81no—
250C2×C8—81no—
251C2×C8—82no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4—42no—
256C22⋊C4—24no—
257C22⋊C4—42no—
258C22⋊C4—44no—
259C22⋊C4—82no—
260C22⋊C4—82no—
261C22⋊C4—82no—
262C22⋊C4—82no—
263C22⋊C4—82no—
264C22⋊C4—82no—
265C42—81no—
266C42—81no—
267C42—82no—
268C42—82no—
269C42—82no—
270C23—22no—
271C23—22no—
272C23—22no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23—88no—
292C23#38711yescharacteristic
293C23#38711yescharacteristic
294C23#38911yescharacteristic
295C23#39411yescharacteristic
296C23#39711yescharacteristic
297C23#40011yescharacteristic
298C23#40011yescharacteristic
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—44no—
335C2×C4—82no—
336C2×C4—82no—
337C2×C4—88no—
338C2×C4—82no—
339C2×C4—82no—
340C2×C4—82no—
341C2×C4—82no—
342C2×C4—82no—
343C2×C4—82no—
344C2×C4#38211yescharacteristic
345C2×C4#38511yescharacteristic
346C2×C4#38811yescharacteristic
347C2×C4#38811yescharacteristic
348C2×C4#39311yescharacteristic
349C2×C4#39811yescharacteristic
350C2×C4#39811yescharacteristic
351C2×C4#40011yescharacteristic
352C8—44no—
353C8—82no—
354C8—82no—
355C8—81no—
356C8—81no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—44no—
378C22—82no—
379C22—82no—
380C22—82no—
381C22—82no—
382C22—82no—
383C22—82no—
384C22#144211yescharacteristic
385C22#205012yes—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—84no—
394C4—162no—
395C4—162no—
396C4#203211yescharacteristic
397C4#203211yescharacteristic
398C2—22no—
399C2—41no—
400C2—41no—
401C2—41no—
402C2—41no—
403C2—41no—
404C2—41no—
405C2#1126511yescharacteristic
406C2#1127911yescharacteristic
407C2#1129411yescharacteristic
subgroupG/H
center, socleC22#1442
commutatorC23×C4C22×C4
Frattini, cosocleC24×C4C23
prime radicalC25#41
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C24×C4 ◁ G
LECSG ▷ C24×C4 ▷ C22 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
21. #1293C4semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#219432
#81082
#81042
#80512
#80092
#79422
#79292